Quadratic Forms With Applications

The scope of Quadratic Form Theory is historically wide although it usually appears almost as an afterthought when needed to solve a variety of problems such as the classification of Hessian matrices in finite dimensional Calculus [1], [2], [3], the finding of invariants that fully describe the equivalence class of a given form in Algebraic Geometry and Number Theory [4], the use of Rayleigh-Ristz methods for finding eigenvalues of real symmetric matrices in Linear Algebra [5], [6], the second order optimality conditions in Optimization Theory [1], [2], [3], the Sturm comparison criteria and the Sturm-Liouville Boundary Value Problems in Differential Equations [5], the kinetic energy or the Hamiltonian in Mechanics.